2y+45=y^2+10y+25

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Solution for 2y+45=y^2+10y+25 equation: 


Simplifying
2y + 45 = y2 + 10y + 25

Reorder the terms:
45 + 2y = y2 + 10y + 25

Reorder the terms:
45 + 2y = 25 + 10y + y2

Solving
45 + 2y = 25 + 10y + y2

Solving for variable 'y'.

Reorder the terms:
45 + -25 + 2y + -10y + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 45 + -25 = 20
20 + 2y + -10y + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Combine like terms: 2y + -10y = -8y
20 + -8y + -1y2 = 25 + 10y + y2 + -25 + -10y + -1y2

Reorder the terms:
20 + -8y + -1y2 = 25 + -25 + 10y + -10y + y2 + -1y2

Combine like terms: 25 + -25 = 0
20 + -8y + -1y2 = 0 + 10y + -10y + y2 + -1y2
20 + -8y + -1y2 = 10y + -10y + y2 + -1y2

Combine like terms: 10y + -10y = 0
20 + -8y + -1y2 = 0 + y2 + -1y2
20 + -8y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
20 + -8y + -1y2 = 0

Factor a trinomial.
(2 + -1y)(10 + y) = 0


Subproblem 1
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2

Subproblem 2
Set the factor '(10 + y)' equal to zero and attempt to solve:

Simplifying
10 + y = 0

Solving
10 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y = 0 + -10
y = 0 + -10

Combine like terms: 0 + -10 = -10
y = -10

Simplifying
y = -10
Solution
y = {2, -10}

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